which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.?\nacute…
which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.?\nacute, because 10²+12²>15²\nacute, because 12²+15²>10²\nobtuse, because 10²+12²>15²\nobtuse, because 12²+15²>10²
Answer
Explanation:
Step1: Recall the triangle - type determination rule
For a triangle with side lengths (a), (b), and (c) ((c) is the longest side), if (a^{2}+b^{2}>c^{2}), the triangle is acute; if (a^{2}+b^{2}<c^{2}), the triangle is obtuse; if (a^{2}+b^{2}=c^{2}), the triangle is right - angled. Here, (a = 10), (b = 12), and (c = 15).
Step2: Calculate (a^{2}+b^{2}) and (c^{2})
(a^{2}=10^{2}=100), (b^{2}=12^{2}=144), so (a^{2}+b^{2}=100 + 144=244), and (c^{2}=15^{2}=225). Since (10^{2}+12^{2}=244>15^{2}=225), the triangle is acute.
Answer:
acute, because (10^{2}+12^{2}>15^{2})